We held our sixth GPU4GEO Julia hackathon on October 07-11, 2024 in Black Forest (DE), focussing on a wide range of Julia topics. Hereafter a glimpse into the progress made by some participants on various Julia-related projects and some visual impressions.
๐ง more news to come!
Chmy.jl - Finite differences and staggered grids
You Wu, Ivan Utkin, Ludovic Rรคss
It has been a fruitful week, where we restructured the package structure and we also further furnished the documentation of Chmy.jl, targeting on the distributed usage of it.
In order to allow users to use all submodules with a single using Chmy statement, we refactored the API to export symbols in submodules explicitly as addressed in PR #51. Instead of relying on an external package such as Reexport.jl, we decided to manually export all relevant symbols to avoid unnecessary package dependencies.
With PR #56, we aim to provide a comprehensive yet beginner-friendly documentation to distributed usage of Chmy.jl for our users. To do this, we provide a conceptual introduction to distributed computing generally under the section Distributed. For more experienced users, one can start with a simple script for solving a 2D diffusion example under the section Using Chmy.jl with MPI.
Convection code
Paul Tackley
A Julia spherical annulus convection program. The program solves the 2D spherical annulus variable-viscosity equations as given in Hernlund & Tackley (2008), on a staggered grid using the direct solver. Some anomalous behaviour is observed relative to the test cases reported in that paper, so more testing/debugging is needed. Once perfected it will be posted online for general use.
Permeability in GeoParams
Pascal Aellig, Jacob Frasunkiewicz
Over the course of the week, we have been discussing and adding Permeability laws to GeoParams.jl. Currently, there are four laws that can now be added and called from the MaterialParams structure. Part one of many has been merged in PR #225, so stay tuned for more over the course of the next few weeks as we implement computational routines to facilitate the writing of two-phase codes.
Implicit solvers with Enzyme.jl
Lorenzo Candioti, Valentin Churavy
We developed a workflow to solve partial differential equations (PDEs) with implicit schemes using the automatic differentiation package Enzyme.jl. Using Enzyme to solve PDEs typically involves spelling out the residual form of the equations and differentiating this function w.r.t. the solution variable. The resulting Vector-Jacobian-Product (VJP, or Jacobian-Vector-Product, JVP) is then used to assemble the sparse Jacobian needed to solve the equations. The newly developed workflow relies on Krylov solvers which only need the JVP (or VJP) as input to solve the system of equations, thus avoiding the computationally expensive part of assembling the full Jacobian. Tested on a simple 1D Diffusion Equation, the new workflow is ca. 1.5x faster compared to the full Jacobian assembly approach.
Matrix-free
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Time Allocations
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Tot / % measured: 989ms / 100.0% 1.07MiB / 71.3%
Section ncalls time %tot avg alloc %tot avg
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iteration 1 989ms 100.0% 989ms 785KiB 100.0% 785KiB
gmres 9 988ms 100.0% 110ms 78.9KiB 10.1% 8.77KiB
jvp 43.3k 276ms 28.0% 6.38ฮผs 0.00B 0.0% 0.00B
forward 10 82.2ฮผs 0.0% 8.22ฮผs 0.00B 0.0% 0.00B
inc 9 44.4ฮผs 0.0% 4.93ฮผs 0.00B 0.0% 0.00B
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Jacobian assembly
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Time Allocations
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Tot / % measured: 1.43s / 100.0% 56.7MiB / 99.2%
Section ncalls time %tot avg alloc %tot avg
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iteration 1 1.43s 100.0% 1.43s 56.2MiB 100.0% 56.2MiB
assembly 9 1.40s 98.2% 156ms 15.0MiB 26.6% 1.66MiB
jvp 90.0k 625ms 43.8% 6.94ฮผs 0.00B 0.0% 0.00B
solve 9 24.8ms 1.7% 2.76ms 40.5MiB 72.1% 4.50MiB
forward 10 73.0ฮผs 0.0% 7.30ฮผs 0.00B 0.0% 0.00B
โโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโโUsing Enzyme.jl to calculate adjoint sensitivies within JustRelax.jl
Christian Schuler, Valentin Churavy, Albert de Montserrat, Pascal Aellig
ParallelStencil.jl has been made compatible with the latest Enzyme.jl version (PR #169 and PR #170). With the help of Enzyme.jl and ParallelStencil.jl the neccessary vector-Jacobian products (VJP) for the adjoint solve in JustRelax.jl can be calculated. Work has also been done to make the adjoint solve work on multiple GPUs/CPUs. The figure shows a viscoelastic falling block example with adjoint sensitivities w.r.t. to the viscosity and density.
New Metal backend for ParallelStencil.jl
Giacomo Aloisi, Samuel Omlin
During the week we have implemented a Metal.jl backend for ParallelStencil.jl! ๐๐๐ This will allow users to exploit their Apple silicon GPUs like the M1, M2 and M3 chips that are available on modern macOS laptops, to use with ParallelStencil for an amazing speedup!
This is the PR #175 with the changes, so stay tuned for a new release soon!